[Formulation en transformation finie du principe d’écart d’équilibre discret : application à l’estimation directe de paramètres à partir de mesures de champs]
La méthode de l’écart d’équilibre (EGM) est une méthode directe d’identification de paramètres de modèles, c’est-à-dire qu’elle ne nécessite aucune résolution du modèle. Elle a été largement étudiée dans le contexte des petites déformations, mais n’a pas fait l’objet d’un examen approfondi pour les grandes déformations. Dans cet article, nous proposons une nouvelle formulation de l’EGM, valable pour les grandes déformations et applicable à la fois aux forces surfaciques et aux forces volumiques, lorsque des mesures plein champ sont disponibles. Notre approche est basée sur une formulation continue et une discrétisation consistante du principe de l’écart d’équilibre récemment proposées. En outre, nous avons développé un pipeline pour quantifier la robustesse de notre nouvelle formulation EGM au bruit, et nous avons comparé ses performances à d’autres méthodes d’estimation classiques, à savoir la méthode « Finite Element Method Updating » (FEMU) et la méthode des champs virtuels (VFM). Notre pipeline de quantification de la robustesse implique la génération de données synthétiques à partir d’un modèle de référence via deux méthodes potentielles : soit en ajoutant du bruit au déplacement de référence, soit en générant des images bruitées et en effectuant un suivi de mouvement avec le principe de l’écart d’équilibre utilisé comme régularisation mécanique. Alors que la qualité de l’estimation utilisant notre nouvelle formulation EGM est faible avec la première méthode de génération de données, elle s’améliore considérablement avec la seconde méthode. Étant donné que la deuxième méthode de génération de données synthétiques reproduit fidèlement les processus expérimentaux, l’EGM, lorsqu’elle est associée au suivi des mouvements avec régularisation de l’écart d’équilibre, fait preuve d’une robustesse raisonnable face au bruit. Il s’agit donc d’une option prometteuse pour l’estimation directe de paramètres à partir de mesures plein champ.
The Equilibrium Gap Method (EGM) is a direct model parameter identification method, i.e., that does not require any resolution of the model. It has been extensively studied in the context of small strains but not thoroughly investigated for large strains. In this article, we propose a novel formulation of the EGM, valid in large strains, and applicable to both boundary and body forces, when full-field measurements are available. Our formulation is based on a recently proposed continuous formulation and consistent discretization of the equilibrium gap principle. Additionally, we developed an estimation pipeline to quantify the robustness of our new EGM formulation to noise, and we compared its performance to other classical estimation methods, namely the Finite Element Model Updating (FEMU) method and the Virtual Fields Method (VFM). Our robustness quantification pipeline involves generating synthetic data from a reference model through two methods: by adding noise to the reference displacement, or by generating noisy images and performing motion tracking with the Equilibrium Gap principle used as mechanical regularization. While the quality of estimation using our new EGM formulation is poor with the first data generation method, it improves drastically with the second method. Since the second method of synthetic data generation closely mimics experimental processes, the EGM, when combined with motion tracking with Equilibrium Gap regularization, demonstrates reasonable noise robustness. Thus, it is a promising option for direct parameter estimation from full-field measurements.
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Mots-clés : Méthode de l’écart à l’équilibre, Problèmes inverses, Grandes transformations, Identification, Quantification d’incertitude
Alice Peyraut 1, 2 ; Martin Genet 1, 2
CC-BY 4.0
@article{CRMECA_2025__353_G1_259_0,
author = {Alice Peyraut and Martin Genet},
title = {Finite strain formulation of the discrete equilibrium gap principle: application to direct parameter estimation from large full-fields measurements},
journal = {Comptes Rendus. M\'ecanique},
pages = {259--308},
publisher = {Acad\'emie des sciences, Paris},
volume = {353},
year = {2025},
doi = {10.5802/crmeca.279},
language = {en},
}
TY - JOUR AU - Alice Peyraut AU - Martin Genet TI - Finite strain formulation of the discrete equilibrium gap principle: application to direct parameter estimation from large full-fields measurements JO - Comptes Rendus. Mécanique PY - 2025 SP - 259 EP - 308 VL - 353 PB - Académie des sciences, Paris DO - 10.5802/crmeca.279 LA - en ID - CRMECA_2025__353_G1_259_0 ER -
%0 Journal Article %A Alice Peyraut %A Martin Genet %T Finite strain formulation of the discrete equilibrium gap principle: application to direct parameter estimation from large full-fields measurements %J Comptes Rendus. Mécanique %D 2025 %P 259-308 %V 353 %I Académie des sciences, Paris %R 10.5802/crmeca.279 %G en %F CRMECA_2025__353_G1_259_0
Alice Peyraut; Martin Genet. Finite strain formulation of the discrete equilibrium gap principle: application to direct parameter estimation from large full-fields measurements. Comptes Rendus. Mécanique, Volume 353 (2025), pp. 259-308. doi : 10.5802/crmeca.279. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.5802/crmeca.279/
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